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Simplifying 3b2 + 18b + 17 = -3 Reorder the terms: 17 + 18b + 3b2 = -3 Solving 17 + 18b + 3b2 = -3 Solving for variable 'b'. Reorder the terms: 17 + 3 + 18b + 3b2 = -3 + 3 Combine like terms: 17 + 3 = 20 20 + 18b + 3b2 = -3 + 3 Combine like terms: -3 + 3 = 0 20 + 18b + 3b2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. 6.666666667 + 6b + b2 = 0 Move the constant term to the right: Add '-6.666666667' to each side of the equation. 6.666666667 + 6b + -6.666666667 + b2 = 0 + -6.666666667 Reorder the terms: 6.666666667 + -6.666666667 + 6b + b2 = 0 + -6.666666667 Combine like terms: 6.666666667 + -6.666666667 = 0.000000000 0.000000000 + 6b + b2 = 0 + -6.666666667 6b + b2 = 0 + -6.666666667 Combine like terms: 0 + -6.666666667 = -6.666666667 6b + b2 = -6.666666667 The b term is 6b. Take half its coefficient (3). Square it (9) and add it to both sides. Add '9' to each side of the equation. 6b + 9 + b2 = -6.666666667 + 9 Reorder the terms: 9 + 6b + b2 = -6.666666667 + 9 Combine like terms: -6.666666667 + 9 = 2.333333333 9 + 6b + b2 = 2.333333333 Factor a perfect square on the left side: (b + 3)(b + 3) = 2.333333333 Calculate the square root of the right side: 1.527525232 Break this problem into two subproblems by setting (b + 3) equal to 1.527525232 and -1.527525232.Subproblem 1
b + 3 = 1.527525232 Simplifying b + 3 = 1.527525232 Reorder the terms: 3 + b = 1.527525232 Solving 3 + b = 1.527525232 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + b = 1.527525232 + -3 Combine like terms: 3 + -3 = 0 0 + b = 1.527525232 + -3 b = 1.527525232 + -3 Combine like terms: 1.527525232 + -3 = -1.472474768 b = -1.472474768 Simplifying b = -1.472474768Subproblem 2
b + 3 = -1.527525232 Simplifying b + 3 = -1.527525232 Reorder the terms: 3 + b = -1.527525232 Solving 3 + b = -1.527525232 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + b = -1.527525232 + -3 Combine like terms: 3 + -3 = 0 0 + b = -1.527525232 + -3 b = -1.527525232 + -3 Combine like terms: -1.527525232 + -3 = -4.527525232 b = -4.527525232 Simplifying b = -4.527525232Solution
The solution to the problem is based on the solutions from the subproblems. b = {-1.472474768, -4.527525232}
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